1 Data

The data is simulated as per the writeup here, except that \(\beta_k\), \(k = 1,2,3\) are fixed.

2 Analysis

We use Bayesian multivariate generalized linear models with correlated group-specific terms via Stan to model the binary outcomes

In other words, the fitted model was specified as:

\[y_{ijk} = \beta0_{jk} + \beta1_kx_i + \epsilon_{ik}\]

    model <- stan_mvmer(
        formula = list(
            y1bin ~ wealthindex + (1 | years) + (1 | hhid)
            , y2bin ~ wealthindex + (1 | years) + (1 | hhid)
            , y3bin ~ wealthindex + (1 | years) + (1 | hhid)
        )
        , data = sim_dflist[[1]]
        , family = list(binomial, binomial, binomial)
    )

3 Results

3.1 Fixed effects

3.2 Marginal Posterior Parameter Estimates Plots

Plots point estimates for each parameter along with credibility intervals. In this case we are plotting the \(50\%\) uncertainty interval (thick horizontal lines) and the \(90\%\) uncertainty interval (thin horizontal lines). In terms of interpretation, the \(50\%\) uncertainty interval identifies where \(50\%\) of the marginal distribution lies for each parameter.

3.3 Intercept and slope

3.4 Year and hhid variance

3.5 Year-specific estimates

3.6 HH-specific estimates

3.7 Covariance and Sigma